ASSA2008 AIDS AND DEMOGRAPHIC MODELS. USER GUIDE (beta version)

Transcription

1 ASSA2008 AIDS AND DEMOGRAPHIC MODELS USER GUIDE (beta version) Originally prepared by Rob Dorrrington, Leigh Johnson and Debbie Budlender of the Centre for Actuarial Research, University of Cape Town, for the AIDS Committee of the Actuarial Society of South Africa (Feedback welcome: Comments to be sent to aids.actuarialsociety.org.za) July 2010

2 Table of contents Table of contents...i 1. Introduction Overview of AIDS modelling...2 DISCLAIMER The structure of the model DIVISION INTO SUBGROUPS PROCESS OF INFECTION Introduction Starting the epidemic Infection assumptions Paediatric infections STARTING POPULATION MORTALITY Non-HIV mortality Survival of adults with HIV Survival of children with HIV FERTILITY Non-HIV HIV and fertility Overall MIGRATION POPULATION GROUPS INTERVENTIONS AND BEHAVIOUR CHANGE Running the model STARTING THE EPIDEMIC PROJECTING Understanding and adapting outputs STANDARD OUTPUTS ADDING OUTPUT STATISTICS The provincial and urban-rural versions of the model THE PROVINCIAL VERSION THE URBAN-RURAL VERSION Changing assumptions and parameters in the model CALIBRATION TIPS...25 Appendices...27 APPENDIX A: SYSTEM REQUIREMENTS...27 APPENDIX B: DESCRIPTION OF WORKSHEETS...28 Assumptions...28 Results...29

3 ii Interventions...30 Population...30 MortTable...30 SexActivity...31 Male HIVTable and Female HIVTable...31 HIVTable...32 Male and Female Adult Survival...32 Male and Female Staging...33 Paediatric Survival...33 Non-HIV Fertility...34 HIV+ Fertility...34 Male Migration and Female Migration...35 FemPRO...35 FemSTD...35 FemRSK...35 FemNOT...36 MalePRO...36 MaleSTD...36 MaleRSK...36 MaleNOT...36 MaleOLD...36 FemOLD...37 Young...37 AIDS Age Profile...37 HIV Prevalence...37 ANC Age Prevalence...37 ANC Age Profile...37 Calibration...38 Cumulative Deaths...38 Deaths...38 Pyramid...38 Mortality...38 Reported deaths Female and Male...38 Copyright...38 APPENDIX C: DESCRIPTION OF WORKSHEETS IN PROVINCIAL VERSION WORKBOOK...39 Initializer...39 EC Common...39 EC Asian...39 Other worksheets...40 APPENDIX D: SUMMARY OF WORKSHEETS...41 APPENDIX E: ACRONYMS...43

4 1. Introduction This guide begins with an overview of modelling of the HIV/AIDS epidemic in South Africa, which is presented in section 2. Section 3 provides information on the structure of the model. It comprises a brief description of the nature and basis of the assumptions, the location of different aspects of the model on the worksheets, and information about which assumptions and values can be changed by the user. Sections 4, 5 and 6 provide instructions on how to use the model. Section 4 describes how to do simple runs so as to get projections for different years. Section 5 describes the standard output, how to interpret it, and how to obtain additional output. Section 6 provides a brief overview of the provincial and urban-rural versions of the model. Finally, section 7 provides information for the more advanced user who wants to change parameters. This section includes a discussion of the calibration that is necessary when making such changes. As, structurally, the different versions of the model are all based on the lite version this manual describes, in the main, the lite version of the model. However, where appropriate, details of other versions of the model are discussed. In addition there are several appendices. Appendix A gives details of the system requirements for running the model. Appendix B lists all the worksheets in the main workbook of the full and lite versions and explains where to find particular values. Appendix C lists all the worksheets in the workbook which paste the set-up assumptions into the full model to create the provincial models and explains where to find particular values. Appendix D is a summary list of all the worksheets, specifying the name and nature of the worksheet, whether it contains values that can be changed by users, and whether its contents change when running the projection engine. Appendix E lists all the acronyms used in the text of this user guide. While reading the guide, it is useful to have the workbook of the model at hand as there are repeated references to different parts and features of the workbook in the text. Although some actuarial or demographic background will be helpful in understanding the intricacies of the model s construction, the model is designed to be useful to actuaries and nonactuaries alike. Users who have no need to make changes to the model and its assumptions, for example those who only want to use the output, may want to skip the detail in sections 3 and 5. Users who want to change the assumptions underlying the model must, however, read through this detail as their changes may have unintended effects. The guide assumes a basic proficiency in using Microsoft Excel. In particular, it assumes familiarity with naming conventions for rows and columns, understanding of concepts such as cells, range names, and macros, and an understanding of the difference between cells containing ordinary data and those containing formulae. 1

5 2. Overview of AIDS modelling Modelling of the AIDS epidemic in South Africa by actuaries began with the so-called Doyle or Metropolitan Life model, which was developed in The model was based on a population hypothetically divided into four groups that differed in terms of the relative ease with which individuals belonging to each group were expected to contract and transmit the HIV. The code for the Metropolitan model is proprietary. The Actuarial Society of South Africa (ASSA) felt that it was desirable for people to have access to a non-proprietary programme which users could alter to suit their needs. In 1996, ASSA therefore released the ASSA500 model. This was very similar in structure to the Metropolitan model with some simplifications to ease programming and comprehension and to shorten run times. The model was primarily designed to make users aware of the likely impacts of the epidemic on mortality and morbidity. In 1998, the AIDS Committee of ASSA decided to develop the model further. There were several reasons for this: The ASSA500 model represented the epidemic in the black African population, rather than the population as a whole; There were concerns about the accuracy of the preliminary results of the 1996 census and there was a need for national estimates that attempted to correct for suspected deficiencies; Many South African demographers were continuing to ignore the impact of AIDS in their projections of the South African population; The ASSA500 model had inherited a number of demographic shortcomings from the Metropolitan model, particularly the assumptions of constant fertility, non-hiv mortality over time and the assumption of no international migration. The result was an Excel 95 workbook called ASSA600, released to the public in early The model was designed to be appropriate for use as a national population model for the Pattern II (heterosexual) HIV epidemic found in South Africa. The base model contained a scenario that reflected its builders best estimates of values for the model parameters and was calibrated to fit the antenatal data up to The naming convention was also changed to allow the user to modify the parameter values, for example for sensitivity analysis and scenario planning. The idea was that alternative version of the model could then be saved as ASSA601, 602, etc. In 2000, the AIDS Committee felt that a further revision of the model was necessary. The update was needed because of increased knowledge about the epidemic, the availability of new data against which to calibrate the model, and greater awareness of the uses to which the model was being put. It was also decided to change the naming convention to reflect the year of the latest antenatal data used to calibrate the model. The resultant ASSA2000 model incorporated the following adjustments reflecting new or updated information about the epidemic: antenatal clinic (ANC) summary results; 1998 South Africa Demographic and Health Survey (SADHS) data, in particular, data on prevalence of STDs and condom usage; improved estimates of the population; and mortality data on the pattern and level of deaths that suggested, in particular, that non-hiv mortality for adults has not improved over time as expected. In addition, the model was altered to: improve the fit to ANC survey data; allow for the possibility of making separate male and female assumptions; model the population groups separately; 2

6 limit the trend in mortality and fertility rates over time; limit future in-migration; change the HIV survival curve to be a function of a Weibull distribution; allow for a bimodal distribution of paediatric HIV survival; and disaggregate the contagion matrix (used in ASSA600) into more measurable and controllable parameters of heterosexual behaviour. These include the probability that a partner comes from a particular risk group, the number of new partners per annum, the number of sexual contacts per partner, the age of the partner and the probability a condom is used. The date in the Model name refers to the most recent antenatal and mortality data used in the calibration of the model. Since the Department of Health embargo the detailed data needed to calibrate the model for six months after they release their report, and the report on the surveys have been released as late as October the model is released invariably some time after the year to which the data refer. The ASSA2008 version of the model is the most recent version of the model to be released. The structure of this model is similar to that of ASSA2003. The following are the most significant changes that have been made: Interventions o PMTCT takes into account slower pace of rollout, and lower uptake of single-dose nevirapine. Roll-out is now in terms of percentage of pregnant women tested and percentage of women on NVP who also receive ART. Also changed the modelling of the impact of interventions on vertical transmission. o Separate ART roll-out rates for men, women and children, and in terms of percentage of new AIDS sick who start treatment. Also allowing for greater reduction in viral load on ART (from 1.76 to 2.8 unit reduction in log of viral load and higher rates of retention on ART. Changed the way condom usage modelled (and IEC rates of rollout and the factor by which the odds of condom usage increases with 100% rollout) Allows for separate HIV survival for adult males and adult females. The survival of untreated adults is now assumed to follow an Exponential distribution rather than a Weibull distribution which leads to a longer mean survival time but with greater variance. Survival of untreated children is assumed to be longer, especially for children infected at or before birth. Because of this the model now allows for the survival of some infected children to adulthood. Like the ASSA2000 model the ASSA2008 model has been produced as a suite of several versions. The lite version, like previous lite versions and the ASSA600 model before them, treats the population of the country as one population group. The full version models each of the four population groups (Asian/Indian, black African, Coloured and White) separately at a national level, and aggregates to produce results for the population as a whole. Notionally the provincial version is the result of the aggregation of the application of the full version of the model separately to each of the provinces, although this aggregation is left to the user to do if desired. It would thus allow for geographic differences in the spread of the epidemic. This user guide is intended for use with all four models. The differences between the lite and full versions will be noted in the text at relevant places. The approaches in the provincial and urbanrural versions are described in section 6. This user s guide is intended for use with the ASSA2008 model, rather than earlier models, although most parts of the guide are also applicable to the earlier versions of the model. As the 3

7 course of the epidemic progresses and more information about it becomes available, the model structure and base scenario will be further updated and future versions of the model will be released. Any feedback on the model in the form of comments and criticisms would be appreciated and can be sent to aids.actuarialsociety.org.za. Disclaimer The model is distributed as a flexible tool to allow researchers to make their own predictions and projections about the HIV/AIDS epidemic. No level of accuracy is implied, nor can the Actuarial Society of South Africa accept any responsibility for the way in which individuals use the model or the results they obtain from it. The model is offered free via the Internet as a public service to anyone who has a use for it. The ASSA2008 model as disseminated has been calibrated to reproduce the patterns of past antenatal clinic survey data and the number of adult deaths. As such, the model represents the triangulation of data from the population census, antenatal survey and registered deaths by some of the country s top actuaries, demographers and epidemiologists. It is not recommended that users alter the assumptions in the model in any way unless they have a very good reason for doing so. If any of the assumptions are altered in any way, the user must ensure that the model is recalibrated to ensure that it remains consistent with the recorded experience to date. Users who have any questions in this regard can consult with the ASSA AIDS Committee (aids.actuarialsociety.org.za). Other sections of this guide note where the user can change particular parameters on the worksheets to reflect a change in assumptions. The following points should be observed when making such changes. In common with previous models one of the features of the ASSA2008 models is the large degree of interdependence of different parameters and assumptions. A change in one will often necessitate a change in others. There are two broad categories of second-level changes. In some cases the first change of value will result in another change automatically, in that other values are dependent, through a formula of the worksheet or a macro procedure, on the changed value. This happens, for example, where proportions must sum to 100%. In these cases, the user does not need to take any action. However, users should note that the automatic changes will only take effect when the user presses the F9 (CALC) key or runs a projection. The automatic CALC function defaults to OFF in the ASSA2008 model to speed up the projection process. In other cases the changed parameter will require a manual change to other parameters and assumptions so as to achieve a fit with the observed values of the ANC surveys, both overall and by age, and the national mortality rates by age. This process of manual changing of parameters to counterbalance previous changes is what we refer to as calibration. Users must be aware of the nature of the information they are changing. Some of the parameters in the ASSA2008 workbook reflect assumptions or observed data such as numbers in the population. These are entered as ordinary numbers on the worksheet. Many other parameters are based on formulae that draw on values in other cells or cell ranges in the workbook. The contents of these cells must not be replaced by numbers. As with ordinary Excel usage, the user can see in the status bar whether a particular cell is the result of a formula or range name reference. In some cases, however, a cell will appear to contain an ordinary number that does not involve a reference or formula but will, in fact, be a record of the previous year s numbers used to project the current year s numbers. This is the case, for example, with all the tables labelled as before. In changing 4

8 values on the worksheets, users must be aware of the very different implications of changing a cell containing a simple value and changing a cell containing a formula or reference or a number generated by previous projections. Guidance as to which values can be changed is given by the colour of the figures. By and large calculated values are in black, while assumptions that affect projection and could thus potentially be changed are in red. Data such as antenatal survey prevalence figures, which do not impact on the computations of the model, are in blue. In the past, incorrect results have been attributed to the Actuarial Society of South Africa or the models in public documents and in the press. In order to prevent this from happening in future, we ask that all users adhere to the following guidelines. If the results have been generated using the models without any alternation, the user should reference them as results extracted from the ASSA2003 (lite, if lite version used) AIDS and Demographic model of the Actuarial Society of South Africa as downloaded [date] from [site address]. If the model has been adjusted and recalibrated, the user must, in addition to the full reference to the model, explain exactly how and why it was adjusted. The user must also make it clear that the resulting estimates are not those produced by the Actuarial Society of South Africa. This must be done in such a way that anyone reading the report understands clearly that the user s results do not represent the views of the Society. Ideally, it should also be done in such a way that another user can replicate the changes and check the projections. 5

9 3. The structure of the model The ASSA model projects year-by-year changes in an initial population profile over a period of years chosen by the user. It does so on the basis of a number of demographic, epidemiological and behavioural assumptions. This section of the guide provides a brief description of the model, its key parameters and assumptions. Any user who wants to change any of the parameters must read this section so as to understand the impact of any proposed changes. The model projects on a year-by-year basis, with each year s projections reflecting changes between 1 July of one calendar year and 30 June of the following calendar year. For the sake of simplicity, each projection year is referred to by a single calendar year rather than by both of the calendar years. The stock numbers for each year reflect the position as at the middle of the respective calendar year, while the flow numbers reflect the change from the middle of that calendar year to the middle of the following calendar year. 3.1 Division Into subgroups The model splits the population by sex and also into three distinct age groupings: young (up to age 13), adult (14-59) and old (60 and above). The full version of the model also splits the population by population group. The adult group is divided into four risk groups, which are differentiated by their level of exposure to the risk of contracting the HI virus through heterosexual activity. These risk groups are: PRO Individuals whose level of sexual activity is such that it is similar to that of commercial sex workers and the level of condom usage and infection with STDs is similar to that of the STD group. STD Individuals whose level of sexual activity is such that their HIV prevalence is similar to someone regularly infected with STDs. RSK Individuals with a lower level of sexual activity, but who are still at risk from HIV in that they have, on average, one new partner per annum and sometimes engage in unprotected sex. NOT Individuals who are not at risk of HIV infection. By definition, someone from the RSK group will not have sex with someone from the PRO group. Further, those in the NOT group have sex only with others in that group or, if they have sex with individuals from other groups, always take effective precautions. The numbers in these risk groups are determined initially according to the proportions appearing on the Assumptions sheet. These proportions are applied equally to all ages over 24. Before age 25, individuals remain in the NOT group until they become sexually experienced. The assumptions have been determined, where possible, on the basis of empirical evidence. Where this was not possible, either educated guesses were made or the assumptions were determined so that modelled results fit observed data such as the antenatal prevalence figures for past years. The latter method of determining values is part of the calibration process discussed later. The age and risk classifications divide the population into the following groups, with each group s calculation done on a separate worksheet within the workbook. In the full version of the model, there is a set of these worksheets for each population group. In the aggregate of the provinces, there 6

10 is a workbook for each province and a set of worksheets for each population group within each province: Young: All individuals aged 0 to 13. The only infections assumed are those arising at birth or from breastfeeding. On their 14th birthday, individuals are allocated to the risk groups according to the assumed proportions on the Assumptions sheet. The model assumes that a proportion of those born to HIV+ mothers are HIV+ at birth. Further, the model assumes that a further proportion of non-hiv babies contract the virus from their HIV+ mothers through breast-feeding. The Young age group is shaded yellow on the worksheets. FemPRO: Female members of the PRO risk group up to age 59, subdivided by duration since infection. FemSTD: Female members of the STD risk group up to age 59, subdivided by duration since infection FemRSK: Female members of the RSK risk group up to age 59, subdivided by duration since infection FemNOT: Female members of the NOT group up to age 59 FemOLD: On their 60th birthdays all individuals are allocated to the OLD class. The duration since infection classification still applies, but no further infections or fertility occur beyond this age. The OLD worksheets are a run-off of the population. No one is assumed to survive beyond age 90. The OLD group is shaded in grey on the worksheets. Male***: The same structure as the Fem*** worksheets but with no births. The total population is allocated between male and female and over the age range according to the distributions given in the Population worksheet. While it is possible to measure, to some extent, the size of the STD group and, to a lesser extent, the PRO group, the RSK and hence NOT groups are hypothetical constructs whose size is set to reproduce past patterns of prevalence through the calibration process. 3.2 Process of infection Introduction Diagram 1 displays how individuals move from state to state under the action of the model. Certain transitions are assumed to be impossible e.g. moving from HIV+ to HIV-; and becoming infected after age 60. The model allows for the inclusion of migrants in all risk groups and at all ages. Migrants are assumed to have the same duration since infection profile and prevalence rate as nonmigrants of the equivalent risk group. It should be noted that in the diagram, the category, HIV+Births includes children who were infected perinatally and those that were infected by breast milk. 7

11 Young (0-13) HIV- Births HIV - Young HIV+ Births HIV + Young Migrants (0-59) Adult (14-59) NOT RSK STD PRO Imported HIV Increasing sexual mobility Increasing risk of HIV infection Migrants (Aged 60+) Old (60+) HIV - Old HIV + Old Deaths Normal Deaths AIDS Deaths Diagram 1: A schematic diagram of the lite model The heterosexual interaction and hence spreading of the virus is modelled taking into account the following, given the person is from a particular risk group: the chance that the partner is from a particular risk group, the chance that the partner is in a particular stage of disease, the number of new partners per year, the number of contacts per partner and the probability of transmission if no condom used (given the risk group of the partner), and the probability that a condom was used. The number of new partners per year and the number of contacts per partner for females at a particular age are a function of a sexual activity curve. This curve was chosen such that the 8

12 pattern of HIV infections of pregnant women assumed by the model to be attending antenatal clinics is more or less the same as the results of the ANC surveys Starting the epidemic Infection is introduced into the PRO risk group via the number of male and female infected imports in the lite model (cells C27 and D27 on the Assumptions sheet). Smaller numbers are used for each of the population groups in the full version of the model to allow for both the smaller size of the populations as well as possible lags in the start of the epidemic. These imports are not added to the population, but rather used to create HIV prevalence of partners in the initial years and hence start the epidemic. The number of imported HIV need not be a whole number or even greater than one. This feature allows the model to cater for situations where the starting date of the epidemic is before or after 1985, by simply changing the size of this number Infection assumptions The epidemic spreads through the population at risk by assumed infection of non-infected individuals within and between groups. The rate of spread of the infection is controlled by assumptions about two key factors, namely the amount of sexual activity, and a range of factors determining the probability of infection. The distribution of female sexual activity by age is represented in the model by the sexual activity curve, which is found on the SexActivity sheet. The curve involves an assumption about the relative sexual activity by age for females. The curve is negatively-skewed bell-shaped with the following form: 2 b( x a) ( x c) e S( x) = c where a (the position factor) is reflects, in part, the average age of first sexual intercourse b (the shape factor) is set, in part, to reproduce the shape of prevalence by age from the antenatal results as well as the age distribution of AIDS cases and AIDS deaths c (the scale factor) is set so that the average of S(x) is 1. The activity of males is a function of that of females and the age of their partners. By varying the shape of the curve, the distribution of the new HIV infections by age is adjusted (separately for different population groups and province in the two other models). The user can manipulate both a (position) and b (shape) factors. The shape and position factors are recorded in column B of the SexActivity sheet. The default values for a and b for the female curve have been set to reproduce the age distribution of ANC HIV prevalence age distributions over time. The reasonableness of the male curve can be checked against the age distribution of reported male AIDS cases circa When changing the shape of the curves and the age distribution of partners of females, the user should ensure that the consistency between the number of deaths and number of AIDS cases still holds. This can be checked by looking at the ANC Age Profile and AIDS Age Profile worksheets and ensuring that the dotted curves (actual figures) are reasonably close to the solid ones (modelled figures). ASSA2008 models sexual behaviour, and thus the probability of infection, on the basis of a combination of several components, as follows: - a matrix showing the probability that a male partner is from a particular risk group; 9

13 - a matrix of male-to-female transmission probabilities per sexual contact for various combinations of risk group encounters; - a matrix of female-to-male transmission probabilities per sexual contact for various combinations of risk group encounters; - a matrix showing the number of new partners per year and the number of contacts per new partner per year; - a matrix showing the probability that a female partner is from a particular risk group; - a matrix of condom usage for each risk group by age; - the effectiveness of condoms; and - a matrix of relative frequencies of sex, relative odds of condom use and relative levels of HIV infectiousness, in different stages of HIV disease (these stages are defined in sections below). These components are all recorded on the Assumptions worksheet. All the above information is then brought together in the following formula: The probability of someone in risk group i, aged x becoming infected in a year is n s( y) D ij t 1 a( x) 1 wij h( y x) ptj ( y) [ 1 Ttij ( y) ] 1 w ij j= 1 y= 14 t= 1 j= 1 y= 14 p j ( y) h( y x) mi s( x) where a (x) is the multiple by which the probability of HIV infection per partnership increases in women aged x (for women over 25 and for men, the value of this parameter is set at 1) w is the proportion of the individual s partners that are in risk group j ij p j ( y) is the proportion of the individual s y-year old partners, in risk group j, that are HIV positive p tj ( y) is the proportion of the individual s y-year old partners, in risk group j, that are HIV positive and in stage t of disease t is the stage of disease (stages 1 to 4 correspond to the four stages of the WHO Clinical Staging System, stage 5 comprises individuals on anti-retroviral treatment, and stage 6 comprises individuals who have discontinued anti-retroviral treatment) h ( y x) is the proportion of the individual s partners that are aged y n is the number of sexual contacts the individual is likely to have per partner in risk group j ij s (x) is an index of the level of sex activity at age x m i is the number of sexual partners the individual has per year D is the factor by which the amount of sex is reduced in stage t of disease t T tij ( y) is the probability that an HIV positive y-year old, in stage t of disease and in risk group j, transmits the virus to a partner in risk group i, during a single act of sexual intercourse. The factor T tij ( y) can be expanded as follows: [ 1 ( 1 [ 1 f ( y ] R ) e ] Ttij ( y) = rij. I t j ) where t 10

14 r ij is the probability that the individual will be infected if they engage in a single act of unprotected sex with an individual in risk group j f j ( y) is the probability that the partner uses a condom e is the effectiveness of condoms in preventing HIV transmission I t is the factor by which the risk of transmission (per act of unprotected sex) is increased in stage t of disease R t is the factor by which the proportion of sex acts that are unprotected is reduced in stage t of disease. (All parameters, with the exception of e, ( y), I t, D t and R t, are gender-specific. Many of the parameters also change value over time.) f j The combination of components allows the model to be used to test the impact of interventions that attempt to change one or more of these variables Paediatric infections Twenty percent of babies born to infected mothers are assumed to be infected at birth. A further 16% of those born to infected mothers not infected at birth are assumed to be infected via breast feeding. The median time of survival of those infected perinatally is 4.74 years and that infected via breastfeeding years in 1985, and increases slightly after that. These assumptions were chosen to be consistent both with the distribution of paediatric deaths by age assumed by the UNAIDS/WHO Reference Group on Estimates, Modelling and Projections, and empirical evidence on the proportion of children of infected mothers who get infected. The user can modify the proportion of births assumed to be infected and the proportion assumed to be infected by mother s milk on the Assumptions worksheet (cells X24 and X25). The relevant table is fourth from the top on the left of the worksheet. 3.3 Starting population The starting population reflects the actual population as at 1 July This was derived by a process of reconstruction linking estimates of the population in 1970 to those of the census population in 1996, ensuring consistency with estimates of fertility and mortality rates derived independently and between the numbers of males and females in various age groups. The current provinces did not exist in For the provincial version of the model, it was therefore necessary to reconstruct the base population that could be expected to have been within these boundaries in that year. This was done by taking into account a remapping of the 1991 census into the new boundaries and the patterns of inter-provincial migration between 1985 and Mortality The mortality data is found in the MortTable worksheet. The initial rates of mortality apply on for the year centred on 1 January 1986, to be consistent with a starting population six months earlier at 1 July the previous year Non-HIV mortality The non-hiv probability of death and probability of becoming infected are used in a multiple decrement life table that applies to individuals not infected by HIV. 11

15 The model uses a table of estimated mortality rates at each age for each of the years 1985 to After 2007, mortality rates are projected to trend logistically to ultimate rates at a rate determined by a mortality improvement factor using the following formula: (a b) x (c (CurrYear 2007) ) where a = the mortality rate in 2007 b = the ultimate mortality rate c = the mortality improvement factor. This formula is contained in the lookup formula which can be found in the table of current year non-aids mortality in the MortTable worksheet. The user can alter the tables of mortality rates for the years to 2007, the ultimate rates of mortality, the mortality improvement factor, and the formulae for interpolating future rates of mortality for all ages on the MortTable worksheet. The relevant formulae are found in the table headed Current Year=X Non-AIDS Mortality Rates, and the ultimate mortality rates and mortality improvement factor. In the full version of the model, these changes need to be made to the population group specific MortTable sheets Survival of adults with HIV In the absence of anti-retroviral treatment, adults are assumed to progress through four stages of disease before dying from AIDS. These four stages correspond to those defined in the WHO Clinical Staging System. The effects of anti-retroviral treatment (ART) are modelled by introducing a further two stages, which represent people receiving treatment and people who have started treatment but subsequently discontinued treatment. Descriptions of these six disease states are given in the table below. The first two stages are largely asymptomatic. Symptoms occur more frequently in stage 3, and include weight loss and oral infections. People in stage 4 experience a range of more severe conditions, such as pneumonia, extrapulmonary TB and wasting syndrome. These conditions are referred to collectively as AIDS. HIV stage Description 1 WHO stage 1: Acute HIV infection 2 WHO stage 2: Early disease 3 WHO stage 3: Late disease 4 WHO stage 4: AIDS 5 Receiving anti-retroviral treatment 6 Discontinued anti-retroviral treatment The possible transitions between these stages are shown in the figure below. In the absence of treatment, individuals are assumed to progress through each of the four WHO stages sequentially, before dying from AIDS. Individuals who initiate ART are assumed to do so at the time that they experience their first AIDS-defining illness, and move into stage 5 on initiating ART. People may die from AIDS while receiving ART or may discontinue treatment before dying from AIDS. 12

16 Stages 1-3: Incubation period Stage 4: AIDS sick Stage 5: Receiving ART Stage 6: Off ART Stage 7: AIDS death The time spent in each of the first four stages and the sixth stage is assumed to follow an exponential distribution. The median and shape parameters for the Weibull distributions are specified in the top left table in the Male and Female Adult Survival worksheets (since the Weibull distributions each have a shape parameter of 1, they are each effectively exponential distributions). The median parameters are assumed to vary according to the age at infection, and the parameters are therefore set separately for three different age bands: 14 to 24, 25 to 34 and 35 or older. For stage 5, rates of transition into stage 6 and rates of AIDS mortality are determined by the ART Assumptions and ART mortality adjustment factors tables on the Interventions worksheet. The ART Assumptions table gives annual probabilities of death and transition to stage 6. The ART mortality adjustment factors table adjusts the mortality rates faced in stage 5 that apply over each successive year of ART rollout. On the basis of the above assumptions, the median time from infection to death (in the absence of non-aids mortality) is calculated in the Male and Female Adult Survival sheets. Ignoring the effects of non-aids mortality, in 2010, the median survival is roughly years for adults (male and female) infected when under the age of 25, 12.11years for adults infected when between the ages of 25 and 34, and years for people infected when over the age of 34. These calculated medians are shown in the Assumptions sheet, in the table fourth from the top on the left hand side of the sheet. They should not be changed by the user as they are calculated from values found elsewhere in the workbook Survival of children with HIV The modelling of the survival of children infected with HIV is similar to the modelling of survival of adults. The key difference is that instead of using a four-stage system to classify individuals prior to ART initiation, we use only two stages: pre-aids and AIDS. It is assumed that the time spent in the AIDS stage as well as the time spent in the ART discontinued stage, follow an exponential distribution. The median and shape parameters for each of these stages are specified in the top left table of the Paediatric Survival sheet. It is assumed that children infected perinatally (i.e. infected at birth) experience more rapid disease progression than children who are infected through mother s milk. Assumed median parameters are therefore specified separately for these two modes of transmission. The rates of transition from pre-aids to AIDS, the rates of AIDS mortality while on ART and the rates at which ART is discontinued are assumed to be constant, except during the first six months on ART. These rates of transition can be altered in columns E and F of the Paediatric Survival worksheet (in the second and third tables on the left-hand side). On the basis of the above assumptions, the median time from infection to death (in the absence of non-aids mortality) is calculated in the Paediatric Survival sheet. Ignoring the effects of non- 13

17 AIDS mortality, in 2010, the median survival is roughly 7.29 years for children infected perinatally and years for children infected through breastmilk. 3.5 Fertility Non-HIV The parameters relating to fertility of those not infected are found on the Non-HIV Fertility worksheet. Overall age-specific fertility rates are determined in a similar way to the mortality rates, with a table of estimated age-specific fertility rates for the period to 2006, after which rates are determined by interpolating between the rates in 2006 and the ultimate rates. The first table in this worksheet provides non-hiv fertility rates for each of the four risk groups for the current year by taking into account the relative fertility of women in each age group and the proportion of women in the various risk groups at that age. The relative fertility factors can be found in the second table from the top left of the Assumptions worksheet. The results are shown in columns B, C, D and E in the non-hiv fertility sheet. The relative fertility factors for the PRO, STD and RSK groups can be changed on the Assumptions sheet. The factor for the NOT group should not be changed as it is derived from the fertility rates for the other three groups. The model assumes that PROs have a lower fertility rate than STDs, who have a lower rate than RSKs, who, in turn, have a lower rate than NOTs. Although this may seem counter-intuitive, the argument for the assumption is that, in order to maintain a highly sexually active life-style, PROs would probably use contraception or abort foetuses. In addition, there is evidence suggesting that STDs may lead to lower fertility. On the other hand, if awareness of contraception is high, then individuals choosing to have children are more likely to be in stable relationships and therefore at reduced risk of contracting HIV. It is unlikely that the relative fertility rate assumptions have a great impact on the results, with the possible exception of the number of infants born HIV-positive HIV and fertility These parameters are found in the HIV+ Fertility worksheet. The model allows for the impact of the duration of infection on fertility by multiplying the non- HIV fertility rates by a factor determined as follows: ( ) adjustment factor = a b c d where a = factor allowing for the bias, particularly at the younger ages, arising from the fact that those falling pregnant are those having sex and not using condoms b = factor allowing for an initial impact of the virus on fertility c = factor allowing for the impact of the virus on fertility over time d = duration of infection in years The first three factors can be changed in the columns entitled Start Ratio, Initial Impact and Reduction Factor towards the right of the worksheet (columns AH to AJ) Overall The births resulting from this fertility are split into males and females according to the assumed proportion of births that are male. This proportion is found on the Assumptions worksheet. The relevant table is fifth from the top, on the left side of the worksheet. The births populate the age 14

18 zero cells in the next step of the projection via the Young sheet. The proportion of births that are boys can be changed by the user but will have minimal effects on the workings of the model. 3.6 Migration The migration-related variables are found on the Male Migration and Female Migration worksheets. For ease of computation, the model assumes that all migration takes place at the end of the relevant projection year. Migrant can refer to both immigrants and emigrants. The figures in the Male Migration and Female Migration worksheets represent net immigration (i.e. in-migrants less out-migrants). The starting population was constructed to include all migrants received up to Migrants are apportioned to the four risk groups according to the proportions in the Assumptions sheet. These are found in the table third from the top on the left side of the worksheet. Currently these proportions are set to be the same as those of the receiving population but the values can be changed by the user. Migration after 2000 is assumed to fall from its 2000 level, logistically, towards close to zero over a 30-year period. 3.7 Population groups The ASSA2003 lite model does not distinguish between the different population groups defined during the apartheid era, namely African, Coloured, Indian and White. The full version of the model allows for separate modelling of the epidemic in the four population groups (sheets identified by Black, Coloured, Asian and White ). This feature of the model was developed in response to user demand. This demand was motivated, in part, by the observation that the impact of the epidemic is very different in the different groups. These differences constitute one of the reasons for differences between the prevalence in the Western and Northern Cape on the one hand and the other provinces on the other. Further, some users wanted to extrapolate the results of the model to socio-economic groups, and geographic sub-regions, and population group is thought to be a useful proxy for these in South Africa. There were thus both demographic and economic reasons for modelling the epidemic in terms of population groups. Developing this aspect required a number of demographic assumptions. The disaggregation presents significant challenges during calibration of the model. Unfortunately, very limited data exist about the impact of the epidemic in the different population groups. Mortality data have not been published on a population group basis since 1990, and the ANC data have not been published in disaggregated form since The mortality data have, since 1998, again been collected on the basis of population group but have not yet been published. The ANC survey continues to collect information on population group. This information is not publicly available, but ASSA s AIDS Committee has been given access to data for 1997 to The model has been fitted to these data and to data from private sector company testing and insurance testing by taking into account differing levels of STDs and condom usage. 15

19 3.8 Interventions and behaviour change The model allows for the effect of interventions (prevention and treatment programmes) on sexual risk behaviours, probabilities of HIV transmission and HIV survival. Currently, five interventions are modelled: improved treatment for sexually transmitted diseases (STDs); information and education campaigns (IEC) and social marketing; voluntary counseling and testing (VCT); mother-to-child transmission prevention (MTCTP); and anti-retroviral treatment (ART). The user can choose which of these interventions are introduced in the projection by entering Yes or No for each intervention in the top left table in the Interventions worksheet. In the table to the right of this, the user can specify the year in which each intervention is assumed to be introduced, and the rates at which each intervention is assumed to be phased in. These rates can be thought of as the proportions of the population that have access to the prevention or treatment programme considered in each year after the initial introduction of the programme. In the default scenario, it is assumed that all five interventions are introduced, but at different times and at different rates of phase-in. The Interventions sheet also contains assumptions about the effect of each intervention. The table below summarises the effects of each intervention in terms of the key epidemiological parameters in the model. It is assumed that all individuals participating in an MTCTP or ART programme would receive counselling and testing prior to joining the programme (the extent of this can be set by the user). The behavioural changes that occur under VCT are therefore assumed also to occur under MTCTP and ART scenarios. Improved STD treatment lowers the probability of HIV transmission, because other STDs enhance the risk of HIV transmission when present in either the HIV-negative or HIV-positive partner. Anti-retroviral treatment also lowers the probability of HIV transmission, because this treatment lowers the concentration of HIV in the body, and hence renders recipients less infectious. Intervention Condom usage Frequency of sex Probability of sexual transmission Probability of motherto-child transmission Survival with HIV IEC and social marketing Improved STD treatment VCT MTCTP Anti-retroviral treatment The table second from the top shows adjustment factors that apply to the rates of mortality shown in the ART Assumptions table (lower down on the Interventions worksheet) over each year of ART rollout. Information and education campaigns are assumed to be the main reason for the dramatic increases in condom usage that have been observed in South Africa over the last decade. It is currently assumed that with the maximum possible roll-out of these campaigns, a 35-fold increase in the odds of condom usage from 1985 levels would occur. This assumption can be changed in the table third from the top in the Interventions worksheet. 16

20 Substantial improvements in the treatment of STDs have occurred since 1994, particularly with the introduction of syndromic management protocols in the public health sector. Since STDs occur more frequently in the higher-risk groups, the effect of the improved treatment is assumed to be greater in the high-risk groups than in the low-risk groups. These assumptions can be changed in the table fourth from the top in the Interventions sheet. The assumed effects of VCT are specified separately for people who are not at risk of infection, people who are at risk of HIV infection, and people in each stage of HIV disease. Individuals who are at risk of infection are generally more likely to be tested than those who are not, and behaviour change following VCT tends to be more significant when people test positive particularly in the later stages of disease. The user can specify the rates at which untested individuals receive testing when there is 100% access to VCT services, and the reductions in unsafe sex for individuals who receive VCT. In addition, the model allows for individuals who test negative to be retested at a later stage, by moving a proportion back into the untested population each year. There is also allowance for a wearing off of the benefits of VCT over time, as individuals gradually forget what they have learnt through the VCT programme and revert to their former sexual practices. All of these assumptions are specified in the table fifth from the top of the Interventions worksheet. The rate at which VCT is accessed is increased if an ART or MTCTP programme is introduced. Individuals participating in these programmes would be required to undergo counselling and testing, as explained previously. In addition, allowance can be made for greater utilisation of VCT services among individuals who are not yet eligible for ART (because they are HIV-negative or still in the early stages of disease), if ART is available. In the default scenario, however, we assume that there is no such increase. Mother-to-child transmission prevention is assumed to reduce both the proportion of children infected perinatally and the proportion infected by breastmilk. These assumptions, together with the assumed proportions of women agreeing to participate in the MTCTP programmes, are specified in the table sixth from the top of the Interventions worksheet. The most significant effect of anti-retroviral treatment is its effect on HIV survival. The reduction in AIDS mortality is modelled by introducing two further disease states, as described in sections and A further benefit of ART is that it reduces the frequency of AIDS-defining illnesses in adults and children by approximately 75%. The model also allows for the reduction in viral load that results from ART, and the associated decline in HIV infectiousness for people on ART. The only potentially negative impact of ART is that people may practise less safe sex if they perceive HIV/AIDS to be less of a threat when they have access to ART. The model therefore allows for a degree of reversal of the benefits from the social marketing programme when ART is available. (In the default scenario, however, it is assumed that there is no adverse behaviour change as a result of ART.) All of these assumptions regarding the effects of ART are specified in the table seventh from the top in the Interventions worksheet. The rates of mortality and discontinuance while on ART are shown in the table. The rates of transmission at the other stages are shown in the top left tables in the Male and Female Adult Survival worksheets and Paediatric Survival worksheets. 17